Method of and apparatus for performing computations



July 21, 1964 T. A. BRI-:NDLE 3,141,959

METHoD oF AND APPARATUS PoR PERFORMING coMPuTATIoNs Filed May 3. 1960 2 Sheets-Sheet 1 N .mtl

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July 21,v 1964 r. A. BRENDLE 3,141,969

METHOD oF AND APPARATUS PoR PERFORMING coMPuTATIoNs United States Patent OV 3,141,969 METHOD F AND APPARATUS FUR PERFORMING COIVIPUTATIUNS Thomas A. Brendle, Mahwah, NJ., assigner to Curtiss- Wright Corporation, a corporation of Delaware Filed May 3, 1960, Ser. No. 26,474 2 Claims. (Cl. 23S-193) This invention relates to a method of and apparatus for performing computations. More particularly this invention relates to a method of and apparatus for performing a multiplicity of ditferent types of computations.

An object of this invention is to provide a method of and apparatus for performing a multiplicity of computations such as nding logarithrns, extracting square roots, summations, divisions and multiplication in which time is utilized as an independent variable.

A further object of this invention is to provide a method of and apparatus for performing a multiplicity of different computations utilizing rst order time constant networks.

Yet another object of this invention is to provide a method of and apparatus for duplicating the relationships which hold when the expression Vl/ V3=V2/ V4 utilizing first order time standard networks and solving the general equation V1(V2+V4)-V2(V1|V3)=0.

Another object of this invention is to provide a method of and apparatus for duplicating the relationships which hold when the quantity Vl/ V3 equals the quantity V2/ V4 as intervals of elapsed time and utilizing the intervals of elapsed time to perform a multiplicity of computations.

Still another object of this invention is to provide a method of and apparatus for performing a multiplicity of computations utilizing time standard networks arranged in an automatic, null balance closed loop system.

The method of duplicating the relationships which hold when the quantity V1/V3=the quantity V2/ V4 utilizing this invention may include the steps of charging a voltage storage device on a transient between a voltage potential Vl and a voltage potential V3, and interrupting the transient charge when the voltage in the voltage storage 3,141,969 Patented July 21, 1964 Cice error voltage is zero whereby the value of the adjusted voltage equals the required function.

A basic computer circuit for duplicating the relationships which hold when Vl/ V3=V2/ V4 may include a time standard network such as a rst order RC (Resistor- Capacitor) or RL network (Resistor-Inductor) connected in series with a source of voltage or current V3. A switch or gate connects or disconnects an unknown voltage V1 across the capacitor C of an RC network, for instance. When the gate is closed the voltage V1 is transferred to the capacitor and when the gate is opened, the capacitor charges on a transient between the voltages Vl and V3. Electrical means connected to the time standard network interrupts the transient charge of the voltage Vc on the capacitor as the voltage Vc passes through an arbitrary value such as zero. At the instant the voltage Y Vc equals zero the time of charge T equals device passes through an arbitrary value such as zero, at

which instant the time interval of charge T of the voltage storage device equals V1 Vl-i-V3 charging a second voltage storage device on a transient between a voltage potential V2 and a voltage V4, interrupting the transient charge as the voltage on said second voltage storage device passes through zero, at which instant the time interval of charge T2 equals V2--i- V4 comparing the time intervals T1 and T2 and simultaneously generating an error voltage equal to the difference between said time intervals and adjusting at least one of the voltages Vl, V2, V3 and V4 until Tl=T2 and the R101 10g llfV-S the relationships to be duplicated.

A closed loop, null balance computer for making computations utilizing the relationship between the period or elapsed charging time and voltage existing across a rst order RC network may include rst and second basic computer networks RlCl and R2C2 respectively connected in a null balance, pulse repetition system. Gating means connect and disconnect to rst RC network, RlCl, with a source of voltage to charge the capacitor on a transient between the voltages V1 and V3. A voltage trigger comparator receive the output voltage Vc across the capacitor and interrupts the transient charge at the instant Vc equals zero. The elapsed time of charge T1 equals Vl RO' log W3 In a similar manner the second RC network R2C2 is charged on a transient between voltages V2 and V4. A voltage comparator trigger interrupts the transient charge as it passes through zero. The time of charge equalling R202 10g m-T A differential amplifier connected to the voltage comparator triggers compares and generates an output voltage proportional to the difference between the time intervals Tl and T2 which equals the desired function of the voltages Vl, V2, V3 and V4, and which when fed back into the networks RlCl and R2C2 for at least one of the voltages Vl, V2, V3 and V4 balances the computer, at which time T1=T2.

These and many other objects will become apparent from the following description of an embodiment of the invention taken in view of the following drawings in which:

FIG. l is an electrical schematic of the invention illustrating a basic computer network.

FIG. 2 is an electrical schematic of the invention showing a closed loop, null balance computer circuit.

FIG. 3 is an electrical schematic of a voltage comparator trigger used in the computer circuit shown in FIG. 2.

FIG. 4 is an electrical schematic of a modied version of the invention shown in FIG. 2 including a ilip flop controlled switching system.

FIG. 5 is a chart illustrating the logic of the operation of the switching system of the computer shown in FIG. 4.

FIG. 6 is a diagram illustrating the waveform of the output voltage VTl of the voltage comparator trigger shown in FIG. 4. y

FIG. 7 is a diagram illustrating the output voltage of the symmetrical flip flop utilized in the computer circuit shown in FIG. 4.

. Y 3 The principle of operation of this invention is based on the condition that if V1/V3 equals V2/ V4 then the following relations hold:

which is the general computer equation (4) V2(V1+V3) V1(V2+V4)=0 A multiplicity of computations may be performed utilizing the aforementioned relationships. For instance the above relationships (l-4) may be utilized to find the square root of a quantity represented by a voltage Vx as follows:

Assuming V1=Vx, V2=Vo, V3=Vo and V4=Vr and inserting these values into (4) yields 0 Vr being unity. This is the desired result.

Similarly many other computations such as multiplication, summations, iinding logarithms etc. may be performed utilizing the relationships (1-4) by choosing the proper values for the quantities V1, V2, V3 and V4, once the relationships (1-4) have been duplicated.

Referring to FIG. 1 a basic computer network for duplicating the relationships which hold when Vl/ V3=V2/ V4 is shown. The basic computer network comprises, for instance, a rst order RC time standard network which comprises a resistor R, a capacitor C and an adjustable voltage source V3. An unknown voltage V1 is connected across the capacitor through a solid state switch or gate which is opened and closed by suitable means not shown.

The switch or gate is closed for a conduction interval just long enough for the voltage Vl to be transferred to the capacitor C at which time the Voltage Vc across the capacitor C equals the voltage Vl. At the end of the charging interval and when the switch gate is opened, a transient current It will start to flow in the RC time standard network. The diierential equation describing the network when the switch is open is:

It: e

V3 T 60 (9) IWW-ne substituting this value into (8) gives V3 V1 -1- V3 l (lo) R Ro 65 solving for T,

since RC is a constant V3 T-RUlOgI/ mfs 70 the exact relationship required.

(12) T=K lo Referring to FIG. 2 an analog computer circuit for performing a multiplicity of computations utilizing the relationships represented by the elapsed time of charge T1 of a lirst order RC time standard network is shown. The computer circuit comprises a pair of similar rst order RC time standard networks RlCl and R2C2 connected in a closed loop, null balance, pulse repetition system.

Before describing the circuit shown in FIG. 2 in detail the operation of the computer will first be brieily described.

As stated the principle of operation of the computer is based on certain relationships (Equations 1-3) which it has been shown can be duplicated electrically as the charging time interval T of a capacitor C arranged in a circuit as shown in FIGURE l. By employing two networks RlCl and R2C2 two respective charging time intervals Tl and T2 may be obtained. By employing voltages Vl and V3 with the network RlCl the time interval required for the capacitor Cl to charge from the voltage V1 through zero is expressed as follows:

Similarly the charging time interval required for the capacitor C2 of the network R2C2 to charge from a voltage V2 through zero is expressed as follows:

V4 (14) T2-K log V2+V4 A voltage comparator trigger 13 shown in detail in FIG. 3 interrupts the transient charge of the capacitor C1 at the instant the output voltage VCl of the capacitor C1 reaches zero. At that instant the trigger trips on swinging its output voltage VTl from a positive to a negative value. Similarly a voltage comparator trigger 14 trips on and interrupts the transient charge of the capacitor C2 at the instant the output voltage VC2 of the capacitor C2 reaches zero. When both of the triggers 13 and 14 have tripped on, an And circuit 22 pulses four-diode gates 11 and 12 to again transfer the voltages Vl and 2 to the networks RlCl and R2C2. At this time the gates are opened and the charging time intervals T1 and T2 are again compared.

A differential amplifier 23 compares the trigger voltages VTl and VT2 and generates a voltage V0 which is proportional to the difference vbetween the respective time intervals T1 and T2.V The voltage V0 thus generated is fed back into the networks for one or more of the voltages V1, V2,YV3 or V4 in the Equations 13 and 14. Since cycling of the Vcomputer is continuous, the time intervals T1 and T2 will continue to be cornpared and the voltages Vo adjusted until Tl equals T2 and the closed loop computer circuit is balanced. At this time the voltage V0 reaches a steady state and .equals the required function of the voltages V1, V2,

V3 and V4. By feeding the voltage Vo` in the networks RlCl and R2C2 for one or more of the voltages Vl, V2, V3 and V4 the computer may be utilized to perform a multiplicity of computations such as square root extraction, division, multiplication, summations and finding logarithms.

Referring now to FIG. 2 the input voltage Vl is applied to the network RlCl across a capacitor C1 and ground through a conventional four-diode gate 11. A

-resistor R1 is connected to a voltage source V3 and the capacitor C1 forming an RC time standard network RlCl. In a similar fashion an input voltage V2 is applied to the network R2C2 across a capacitor C2 and ground through a conventional four-diode gate 12, while a resistor R2 is connected to a voltage source V4 and the capacitor C2 forming an RC time standard network R2C2.

As described in FIG. 1, the voltages V1 and V2 respectively are vtransferred to the capacitors C1 and C2 when the gates 11 and 12 open for the correct conduction intervals. The operation of the gates 11 and 12 is conventional and only the operation of gate 11 need be described in detail.

The gate 11 is a four-diode bridge having four corners 11a-11d. The voltage Vl is connected to the opposite corners 11a-c, and is transferred to the capacitor C1 when a positive voltage pulse appears across the opposite corners 11b and d. During this interval the gate 11 is open. When the positive voltage across the corners 11b and d goes negative the gate I1 closes. The gate 12 is opened in a similar fashion to transfer the voltage V2 to the capacitor C2.

Upon a closing of the gates 11 and 12 respectively, the output voltages VCI and VC2 of the capacitors C1 and C2 which are connected to identical voltage comparator triggers 13 and 14, respectively, discharge on a transient toward zero. The voltage comparator trigger 13 which is essentially a high gain amplifier trips on and interrupts the transient discharge of the voltage VCI as it passes through zero as is clearly shown in FIG. 2. An output voltage VT1 of the trigger 13 swings from a positive value to a negative value at the instant the voltage VCI passes through zero. The elapsed time CII interval of charge TI of the capacitor C1 is as expressed in Equation 13.

The voltage comparator trigger 14 trips on in a similar fashion, interrupting the transient charge of the voltage VC2 as it passes through Zero as shown in FIG. 2. The charging time interval T2 of the capacitor C2 is as expressed in Equation 14. An output voltage VT2 of the trigger 14 also swings from a positive value to a negative value at the instant VC2 passes through zero.

The voltage comparator trigger 13 which is identical with the voltage comparator trigger 14 is shown in detail in FIG. 3 and comprises transistors 16, 17 and 18, interconnected and suitably powered to form a high gain amplifier which produces a constant amplitude pulse when the input voltage VCI is negative or zero.

The output voltage VTI of the trigger 13 is shown in FIG. 2 and is a high positive Value during the interval when the capacitor C1 is discharging between V1 and zero. When the voltage VCI is positive, the trigger is in an off state and the transistors 17 and 18 are nonconducting.

When the input voltage VCI, which is applied to the base electrode of the transistor 16, passes through zero, the transistor 17 connected to the emitter of the transistor 16 through a trigger level resistor 19 is arranged to conduct. The exact value of voltage VCI at which the transistor 17 conducts may be adjusted by varying the setting of the trigger level resistor 19.

The transistor 18 remains cut off until the potential at the collector electrode of the transistor 17 exceeds the bias applied to the emitter electrode of the transistor 18 by a level diode 21. This occurs as VC1 passes through zero volts. At that instant the transistor 18 conducts, tripping the trigger 13 to the on state. The output voltage VT1 is instantaneously changed from a posivtive value such as |20 v. to a negative value such as a -20 v. for example. The output voltage VT1 remains at a constant negative value until the gate 11 is opened :(anld the voltage V1 is again transferred to the capacitor As stated the operation of the triggers 13 and 14 is identical, differing only in the trigger input voltage (VCI or VC2) employed and the output voltage derived (VT1 or VT2).

The output voltages VT1 and VT2 are equal in amplitude and opposing when the triggers 13 and 14 are both on or off, and the voltage across the trigger outputs is zero. When the triggers 13 and 14 are'in different states (either on or off), the voltages VT1 and VT2 are adding and the polarity of the resultant voltage across the trigger outputs is i-4O volts depending upon which of the triggers 13 or 14 trips first as determined by the length of the respective time intervals TI and T2.

The output voltages VTI and VT2 of the triggers 13 and 14, respectively, are connected to a conventional and circuit 22 and to a differential amplifier 23 to complete the closed loop, balanced network computer circuit.

The And circuit 22 is a coincidence circuit having two or more inputs to each of which is applied a pulse of common polarity such as VT1 and VT2 and a single output. A pulse appears at the output of the And circuit 22 only when identical pulses (VT1 and VT2) are applied to both inputs. Thus when VT1 and VT2 are both negative, the And circuit 22 pulses both gates 11 and 12 through a transformer 24 to open the gates and again transfer the voltages Vl and V2 to the capacitors C1 and C2, respectively. The complete cycle of the voltages VCI and VC2 is illustrated in FIG. 2.

Referring to FIG. 2 the output Voltage VT1 of the trigger 13 is applied to the differential amplifier 23 and across a capacitor C3 to ground through an input R3 While the output voltage VT2 of the trigger 14 is applied to the differential amplifier 23 and across a capacitor C4 to ground through an input resistor R4. During conditions of balance, that is when the opposing voltages VTI and VT2 which are equal in amplitude are both positive or negative, the voltage VEF across the capacitors 26 and 28 (points E and F in FIG. 2) is zero and will remain zero until one of the triggers 13 or 14 trips and the triggers are in an opposite state. When this occurs, because of the capacitors C3 and C4, the voltage VEF Will rise as an exponential function of time, its polarity indicating which trigger 13 or 14 has tripped.

The differential amplifier 23, which may be of conventional design and need not be described in detail, has a very high common mode rejection ratio and conducts only during the intervals when VT1 and VT2 are opposite in polarity producing an output voltage V0 which is a linear function of the voltage VEF. A polarity inverter 30 such as a pair of center grounded dropping resistors or a grounded cathode vacuum tube circuit, for instance, is connected to the differential amplifier and reverses the polarity of Vo, thus providing both a negative and positive Vo output.

As stated, the output voltage Vo of the differential arnplifier is a linear function of the voltage VEP and it rises until the triggers 13 and 14 are again in the same state at which time the voltage VEF returns to approximately zero. The rate of increase of the output voltage V0 of the differential amplifier 23 is determined by the time constants R3C3 and R4C4 of the input impedance to the differential amplier 23. The amplitude of the voltage V0 is thus determined by the length of time the voltage comparator triggers 13 and 14 are in different states.

Since the triggers 13 and 14 are both in the off state when the voltages VCl and VC2 are positive (the instant the gates 11 and 12 are closed) and reverse to the on state only when the voltages VCI and VC2 pass through zero, the amplitude of the voltage V0 at any instant is proportional to the difference between the respective charging times T1 and T2 that it takes for the capacitors C1 and C2 to charge between the voltages Vl and V3 and V2 and V4, respectively. That is:

V1 -I-V3 V2 -l-V4 When both of the triggers 13 and 14 have tripped on the And circuit 22 pulses the gates 11 and 12, resetting them and commencing a new cycle. v

The adjusted voltage V0 is fed back into the networks RICI and R2C2 for one or more of the voltages V1, V2, V3 or V4 depending upon which computation is to be performed. As the computer circuit cycles the voltage VEF is reduced to approximately Zero, at which time the time intervals TI and T2 are approximately equal. Uti- 7 lizing the relationships which hold when Vl/ V3=V2/ V4 and the circuit of FIG. 2 a multiplicity of computations can be performed by Vchoosing the proper designations and values for the voltages V1, V2, V3 and V4.

Square Root Extractions To extract the square root of a number represented by a voltage Vx for instance the closed loop, null balance, computer network is arranged as follows:

(16) V1= Vx the unknown voltage 17) V2=`l Vo 1 8 V3 Vo 19) V4: Vr (reference voltage) Assuming Vx=9, V equals zero initially, R1C1 equals R2C2 and the gates 11 and 12 are open, the operation of the circuit is as follows:

The capacitors C1 and C2 will charge to the voltages Vx and V0, respectively, at which time an And circuit output pulse will be discontinued, closing the gates 11 and 12. The voltage comparator triggers 13 and 14 will remain in the off state until the input voltages VC1 and VC2 pass through zero. The times required for the capacitors C1 and C2 to charge to zero are T1 and T2, respectively where Since the quantity K in both equations is equal, T1=T2 reduces to 22) VT-T which reduces to (23) V0=\/VxVr and when Note that Vr may be any value desired to give the proper amplication factor for V0.

In the example, since Vx is 9 and Vo is Zero or at a minimum operation voltage for the differential amplifier 23, Tl is greater than T2. The voltage comparator trigger 14 will trip instantaneously and the voltage VT2 will go negative. At that instant, the voltage VEF will start from zero and increase exponentially as a function of time until the trigger 13 trips and the voltage VT1 goes negative.

The output voltage Vo of the diiferential amplifier because of the time constants R3C3 and R4C4 increases linearly during the time interval (T1-T2) to a value of 3 volts. At the instant the voltage VT1 goes negative the And circuit 22 will pulse the gates 11 and 12 through the transformer 24 to again open the gates and charge the capacitors C1 and C2, respectively, for a next cycle of operation.

During the next cycle of operation, the circuit will be balanced, T1 equals T2, and the voltage Vowill remain constant. It is to be noted that by varying the time constant of the input impedance to the differential amplifier 23, the slope and thus the amplitude of the voltage Vo may be varied. In this event the computer circuit will continue to cycle and compare the respective time intervals T1 and T2 until the voltage Vo is adjusted to the proper value and the time intervals T1 and T2 are made equal. At that instant the computer circuit is balanced and Vo equals the required function of the voltages V1, V2, V3 and V4.

In this instance the time constants R3C3 and R4C4 of the input impedance to the differential amplifier 23 are chosen so that the slope of the output voltage Vo is such that the time intervals T1 and T2 are made equal and the computer circuit is balanced in one cycle of operation. Thus, the respective charging time intervals T1 and T2 are simultaneously compared and made equal to provide a symmetric, null balance closed loop, computer circuit.

Division 0r Ratio To perform the computation of division such as Vx/ Vy using the computer circuit of FIG. 2, assume the following:

(25) Vl=Vx (26) Vy=V3 (27) Vr=V2 and T he operation of the circuit is the same as for extracting square roots, and

Vy (29) Ti-R 101 10g -VgJrVx and (30) T2=R2O210gl- VO-i-Vr when the respective voltages VC1 and VC2 pass through zero. Adjusting the Voltage V0 until T1 equals T2 and solving for V0, yields Vr Vy (3U www@ which reduces to (32) or V1/V3 S ummati ons To find the sum of the quantities Vx-l- Vy-l-Vz, for example, using the null balanced computer circuit of FIG. 2, assume the following:

Again solving for T1 and T2 when the voltages VC1 and VC2 pass through an arbitrary value of voltage VA Where VA (Vo-Vz) and (38) T2=R2C2 log the desired relationship. Again the differential amplifier 23 responds to the difference between the time intervals T1 and T2 to adjust the voltage Vo and balance the RC time standard networks R1C1 and R2C2. It is to be noted that the transient voltages VC1 and VC2 across the capacitors C1 and C2, respectively, need not be interrupted at the instant they reach Zero but may be interrupted at some arbitrary value such as VA in this instance.

Obviously, the above circuit can be utilized to find the sum of a greater number of figures by using the voltage Vo in two or more of the balanced networks in a progressive relationship.

Multiplication To multiply the quantities Vx and Vy for instance using the null balanced computer network of FIG. 2, assume the following:

(41) V1=Vx (42) V2=Vr (43) V3=Vo and (44) V4=Vy Solving for Tl and T2 when the voltages VC1 and VC2 pass through zero V (45) TV1-R101 log VWM/.0

and

Vy 46 T2 R202 log VWM/,T Making Vr unity and Tl :T 2 gives (47) V0: VyVx which is the desired result. It is to be noted that when Vx=Vy, the circuit may square the unknown quantity. The differential amplifier 23 responds to the difference between the time intervals T l and T2 and simultaneously adjusts the voltage Vo to the correct value to balance the RC time standard networks RlCl and R2C2.

Referring now to FIG. 4, a simplified schematic of a modified version of the computer circuit of FIG. 2 is shown. The modified computer circuit includes the RC time standard networks RlCl and R2C2, the operation of which is identical to that previously described. The voltages VC1 and VC2 in this instance, however, are connected to a single voltage comparator trigger 13. The voltage comparator trigger 13 is set to trip from the olf to the on state when either of its two inputs VC1 or VC2 is zero or negative and resets when both of its inputs VC1 and VC2 are positive. As before described the output VTl of the trigger 13 is either positive or negative. The output voltage VT1 is shown in FIG. 5 as a series of sharp pulses which are determined by the voltages VC1 and VC2 charging from a positive value through zero. The pulsating output voltage VTl of the Voltage comparator trigger 13 is connected to a conventional symmetrical ip flop 31 which in turn controls a pair of switches 32 and 33. The switches 32 and 33 may be transistorized and act as SPDT switches. They are placed in opposite positions, switch 32 being closed and switch 33 open or vice versa. The switches 32 and l@ 33 are pulsed from one position to the other by the symmetrical flip flop 31 which responds to the pulses in the output voltage VTl of the voltage comparator trigger 13. The logic of the operation of the circuits as shown in FIG. 6 illustrates the manner in which the switches are opened and Vclosed by the ilip flop 31 as the voltages VC1 and VC2 charge through Zero from the voltages V1 and V2, respectively.

A differential amplifier 23 having the proper input impedance as previously described is connected to the symmetrical flip op 31 across a pair of collector resistors 34 and 35. The output voltage of the flip flop 31 is of constant amplitude either positive or negative which is determined by the state of voltage comparator trigger 13.

The diiferential amplifier 23 is arranged to operate on the average voltage output Ve of the symmetrical flip flop 31. Thus when the time intervals Tl and T2 are equal, the average value of the error voltage Ve is zero and the output voltage Vo of the differential amplifier 23 remains constant. When the time intervals T1 and T2 are different, the differential amplifier 23 will adjust the value of the voltage Vo accordingly until Tl equals T2 and the error voltage Ve is zero. The polarity of the output voltage Vo of the differential amplifier 23 is inverted across the dropping resistors 36 and 37.

As shown, the circuit of FIG. 4 is arranged to take the square offa quantity Vx. In this instance assume the following:

, (48) V1: Vx (49) V2=V0 (50) V3=O and (51) V4: Vr

In operation with the power off the transistor switches 32 and 33 are closed transferring the voltages Vl and V2 to the capacitors C1 and C2, respectively. The instant the transistor switches 32 and 33 are energized, the symmetrical ip flop 31 by its inherent feedback trips on to open one of the switches, for instance, switch 32 and close switch 33. At that instant the voltage VC1 of the capacitor C1 will start on a transient charge toward the voltage V0. As the voltage VC1 passes through zero the voltage comparator trigger 13 will trip on to pulse the symmetrical flip ilop 31 and reverse the position of the switches 32 and 33. That is, the switch 32 now closes and the switch 33 opens.

At that instant, both inputs VC1 and VC2 to the voltage comparator trigger 13 are positive and the voltage comparator trigger 13 will reset to the olf state. At that time, however, the voltage VC2 of the capacitor C2 is charging from the voltage Vo toward zero and at the instant the voltage VC2 reaches zero the voltage cornparator trigger 13 will again fire on to pulse the symmetrical flip flop 31 and again reverse the state of the switches 32 and 33 to initial a next cycle of operation.

Each time the trigger 13 pulses the flip flop 31, an output voltage Ve of the flip flop 31 swings between a positive and negative value resulting in a pulsating output as shown in FIG. 7.

Since the waveform of the voltage Ve is symmetrical the average value of the error voltage Ve is zero when the time interval Tl and T2 are equal and varies as a function of the difference between the respective time intervals T1 and T2.

A differential amplifier 23 which has a high common mode rejection ratio operates on the average value of the error voltage Ve to produce a voltage V0, which is applied to the dropping resistors 36 and 37 and inserted into the computer circuit as voltages V2 and V3, in this instance. The circuit will cycle and continuously compare the time intervals Tl and T2 until the differential autres@ l l l 2 amplifier adjusts the voltage V to the value which the second input circuit with V2 substituted for V1, forces the error voltage Ve to zero. At this time the V4 for V3, and VT2 for VT1, said first input following equations hold: circuit including: (52) TIITZ (al) a gate receiving at its input Vl,

5 (a2) means for applying spaced gating pulses to 0T said gate for gating V1 through,

V0 VT (a3) a time constant network receiving as ener- (53) Wll75=5`m gizing potential V3 and the through-gated V1,

and producing output potential which is sub- Solvlng Equanon 53 ylelds 10 stantially V1 while a gating pulse is applied to (54) Vozi/c said gate, and which relaxes from V1 towards V3 upon closure ofthe gate, (a4) a trigger receiving the latter output signal as trigger input signal, for generating VT1 in form of a two-level trigger output voltage pulse train, the trigger output voltage transferring from the first level to the second level when the trigger input voltage attains a predetermined value while relaxing towards V3, and retransferring to said first level as the trigger input voltage recovers to substantially V1, said computing circuit further comprising:

(b) pulse generating means responsive to coincidence which is the required function of the input voltage Vx. Thus, in the modified closed loop, null balance computer circuit of FIG. 4 the time intervals Tl and T2 are determined separately and then compared to produce an error voltage Ve equal to the difference between the respective time intervals Tl and T2. In the null balance closed loop computer circuit of FIG. 2 the gates 11 and 12 are closed at the same instant allowing the capacitors C1 and C2 to charge toward Zero simultaneously to determine the respective time intervals T l and T2.

It is to be noted, however, that the circuit of FIG. 4 may also be arranged to Perform tno computations of of second levels of VT1 and VT2 for generating said division multiplication and summanon by the Proper gating pulses and delivering them via the mentioned selection and insertion of voltages into the circuit for the pulSe applying means to the input circuit gates, Values V1 V2 V3 and V4' Fnrtner the olrolnt of (c) differential integrating means receiving VT1 and FIG. 2as well as FIG. 4may be ut1l1zed to find logarithms VTZ as input voltages and building up V0 as the by disconnecting the differential amplifier in each case and time integral of their difleren7 and using the error Vonagove or VEP ones/[W1 30 (d) means for applying iVo to at least one of said A preferred embodnnont of the lnwnnon nas been input circuits to constitute it at least one of the four shown, but obviously numerous alterations and modicavoltages Vl, V2J V3 V4I whereby to force the rst tions may be made in the light of the above teachings. level durations of VT1 and VT2 substantially to Accordingly it is to be expressly understood that tno coincidence, whence V0 assumes a value correspondspirit and scope of the invention is to be` limited only by ing to the Computed result the spuit and scope of the appended Clanns' 2. A computer circuit. according to claim l, wherein I dann: the gating pulse generating means produces gating pulses 1' A, Closed loop nunbalance computing, cncnli for having uniform width and having separation that is generatmg an output Voltage V0 as a funcnon of Input variable in accordance with the time difference of first voltages V1, V2, V3, V4, at least one of the latter 4,0 level durations of VT1 and VT2 voltages being Vo, said computing circuit comprising:

(a) two like input circuits, one receiving V1 and V3 References Cited in the nl@ of this Patent as input voltages and delivering output voltages VT1, UNITED STATES PATENTS the other receiving V2 and V4 as input voltages and i delivering output voltage VT2, the following or- 2603689 Stevens et al' July 15 1952 2,619,514 Stanton Nov. 25, 1952 ganization of the first input circuit also applying to 2 652 194 Hirsch Sept 15 i953 

1. A CLOSED LOOP NULL-BALANCE COMPUTING CIRCUIT FOR GENERATING AN OUTPUT VOLTAGE V0 AS A FUNCTION OF INPUT VOLTAGES V1, V2, V3, V4, AT LEAST ONE OF THE LATTER VOLTAGES BEING $V0, SAID COMPUTING CIRCUIT COMPRISING: (A) TWO LIKE INPUT CIRCUITS, ONE RECEIVING V1 AND V3 AS INPUT VOLTAGES AND DELIVERING OUTPUT VOLTAGES VT1, THE OTHER RECEIVING V2 AND V4 AS INPUT VOLTAGES AND DELIVERING OUTPUT VOLTAGE VT2, THE FOLLOWING ORGANIZATION OF THE FIRST INPUT CIRCUIT ALSO APPLYING TO THE SECOND INPUT CIRCUIT WITH V2 SUBSTITUTED FOR V1, V4 FOR V3, AND VT2 FOR VT1, SAID FIRST INPUT CIRCUIT INCLUDING: (A1) A GATE RECEIVING AT ITS INPUT V1, (A2) MEANS FOR APPLYING SPACED GATING PULSES TO SAID GATE FOR GATING V1 THROUGH, (A3) A TIME CONSTANT NETWORK RECEIVING AS ENERGIZING POTENTIAL V3 AND THE THROUGH-GATED V1, AND PRODUCING OUTPUT POTENTIAL WHICH IS SUBSTANTIALLY V1 WHILE A GATING PULSE IS APPLIED TO SAID GATE, AND WHICH RELAXES FROM V1 TOWARDS V3 UPON CLOSURE OF THE GATE, (A4) A TRIGGER RECEIVING THE LATTER OUTPUT SIGNAL AS TRIGGER INPUT SIGNAL, FOR GENERATING VT1 IN FORM OF A TWO-LEVEL TRIGGER OUTPUT VOLTAGE PULSE TRAIN, THE TRIGGER OUTPUT VOLTAGE TRANSFERRING FROM THE FIRST LEVEL TO THE SECOND LEVEL WHEN THE TRIGGER INPUT VOLTAGE ATTAINS A PREDETERMINED VALUE WHILE RELAXING TOWARDS V3, AND RETRANSFERRING TO SAID FIRST LEVEL AS THE TRIGGER INPUT VOLTAGE RECOVERS TO SUBSTANTIALLY V1, SAID COMPUTING CIRCUIT FURTHER COMPRISING: (B) PULSE GENERATING MEANS RESPONSIVE TO COINCIDENCE OF SECOND LEVELS OF VT1 AND VT2 FOR GENERATING SAID GATING PULSES AND DELIVERING THEM VIA THE MENTIONED PULSE APPLYING MEANS TO THE INPUT CIRCUIT GATES, (C) DIFFERENTIAL INTEGRATING MEANS RECEIVING VT1 AND VT2 AS INPUT VOLTAGES AND BUILDING UP V0 AS THE TIME INTEGRAL OF THEIR DIFFERENCE, AND (D) MEANS FOR APPLYING $V0 TO AT LEAST ONE OF SAID INPUT CIRCUITS TO CONSTITUTE IT AT LEAST ONE OF THE FOUR VOLTAGES V1, V2, V3, V4, WHEREBY TO FORCE THE FIRST LEVEL DURATIONS OF VT1 AND VT2 SUBSTANTIALLY TO COINCIDENCE, WHENCE V0 ASSUMES A VALUE CORRESPONDING TO THE COMPUTED RESULT. 